Checkout some more links that can help you.
How to retrieve JSON Data Array from ExtJS Store
how to get json data in jquery
help needed retrieving json data with jquery
Retrieving a JSON file using Ajax
These links can help you.
You shouldn't need to do anything special to represent a / in JSON - a string can contain any character except a " or (when not used to start an escape sequence) \.
The problem is possibly therefore in:
the way you parse the JSON server side
the way your parse the HTTP data to get the JSON string
the way you encode the string before making the HTTP request
(I'd bet on it being the last of those options).
I would start by using a tool such as LiveHttpHeaders or Charles Proxy to see exactly what data is sent to the server.
(I'd also expand the question with the code you use to make the request, and the code you use to parse it at the other end).